The present invention relates to improvements in integrated optical waveguide devices (e.g. waveguide lenses, prisms, beamsplitters, etc.) for controlling the propagation of radiation in an optical waveguide. More particularly, this invention relates to the optimal achromatization of such devices, whereby the effect of such a device on propagating radiation is minimally dependent on changes in radiation wavelength over a predetermined wavelength range.
In recent years, considerable attention has been directed to the field of integrated optics and the problems associated with precisely controlling the propagation of radiation in slab-type optical waveguides. A variety of different waveguide devices (e.g. prisms and lenses) have been disclosed for reflecting and refracting a beam of radiation within a waveguide, e.g., for purpose of changing the direction of propagation, shaping the wavefront, or bringing the radiation to a focus. Waveguide lenses are generally classed into four types, viz., mode-index, geodesic, Luneburg, and Bragg-grating. The optical elements of interest here are of those of the mode-index variety.
Mode-index devices control the direction or propagation of a wavefront travalling in a waveguide by controlling the effective refractive index encountered by such wavefront in the waveguide. Such devices can take the form of a shaped overlay of uniform thickness situated atop the waveguide. They are described, e.g., by R. Ulrich and R. J. Martin in Applied Optics, Vol. 10, No. 9, p. 2077 (1971).
Ulrich and Martin describe a three-layer waveguide assembly comprising a glass substrate, a transparent thin-film waveguide disposed over a portion of the substrate, and a surrounding medium or "superstrate", typically air. They note that the propagation of light within the waveguide can be described within the limits of geometrical optics by an effective refractive index, N, whose value depends on thickness of the waveguide. By providing a step change (i.e. a sudden increase or decrease) in the waveguide thickness, and by properly shaping the thickness profile at the step boundary, the direction of propagation in the waveguide can be controlled much like conventional lenses and prisms control the propagation of light in bulk optical systems. Ulrich and Martin mention that, by properly choosing the film thickness at both sides of the step, one can produce either an unusually large wavelength dispersion, or achromatic refraction. While some degree of achromatization may be achieved by appropriately varying the thickness of the waveguide in a three-layer system, the wavelength range over which achromatization can be realized is relatively small, typically less than about 25 nm. Moreover, in a three-layer system where the waveguide thickness is selected to support only a single mode of propagation, relatively minor variations in the waveguide thickness from a nominal value, the sort of variation that is difficult to avoid using conventional fabrication processes, can greatly affect the refractive power of the devices.
The dispersion properties of a four-layer thin-film waveguide assembly are described by D. W. Hewak and J. W. Y. Lit in Applied Optics, Vol. 26, No. 5, p. 833 (1987). In a four-layer assembly, the "step change" in waveguide thickness mentioned above with regard to a three-layer assembly is provided by an optical overlay comprising a material different from the waveguide material. Hewak and Lit present a formula describing the variation in the effective refractive index with respect to any physical parameter with which the refractive index of any layer or the thickness of the guiding layers may vary. They examine the chromatic dispersion of a Luneburg lens, i.e., a mode-index lens comprising a dome-shaped overlay. From their model, they conclude that diffraction limited focusing of such a lens can better be achieved over the 0.70-0.84 micron wavelength range by a three-layer waveguide assembly in which, as mentioned, the overlay is of the same refractive index as the underlying waveguide. There is no disclosure in the Hewak and Lit article of how one might achieve achromatization in a four-layer assembly in which the overlay element has a substantially uniform thickness. Moreover, the discussion of achromatization of their Luneberg lens is limited to spot quality or "spherochromism," not axial or longitundinal chromatic aberration.